System identification and sparse decompositions

Dynamic model learning, also known as system identification, is the process of building a mathematical model of a physical process from experimental data. Such models play a fundamental role in methodological developments across various engineering disciplines, including automatic control, signal processing, AI or mechanics. For example, the availability of a dynamic model is vital for control laws design, simulation/prediction, filtering or diagnostics. The aim of this course is to introduce the main methods for learning dynamic systems from data. The dynamic models covered by this course will be essentially linear, time-invariant, discrete-time and possibly multivariable.

I - Input-output models:

• Estimation methods based on the minimization of the prediction error
• Elements for the analysis: identifiability, persistence of excitation, frequency richness of a signal
• Asymptotic properties of the estimators: consistency, convergence in distribution

II - State-space models:

• Some key concepts of system realization theory
• Essential linear algebraic tools
• Subspace methods